Derive the following relation : `log frac (k_2)(k_1) = E_a/(2.303R) [(T_2-T_1)/(T_2T_1)]`

Differentiate the following w.r.t. x log (x + sqrt(1 + x^2))

For any arbitrary motion in space, which of the following relations are true :- a_averag[v(t_2)-v(t_1)]/(t_2-t_1) (The ‘average’ stands for average of the quantity over the time interval t_1 to t_2 )

For any arbitrary motion in space, which of the following relations are true :- v_average=[r(t_2)-r(t_1)/(t_2-t_1) (The ‘average’ stands for average of the quantity over the time interval t_1 to t_2 )

Rate constant 'k' of a reaction varies with temperature 'T' according to the equation: log k= log A- (E_a)/(2.303R) (1/T) where E_a is the activation energy. When a graph is plotted for log k vs. 1/T , a straight line with a slope of - 4250 K is obtained. Calculate E_a for the reaction (R = 8.314 JK^-1 mol^-1)

Differentiate the following functions w.r.t.x : (e^(2x) - 1)/(e^(2x) +1)

For any arbitrary motion in space, which of the following relations are true :- v_average=(1/2) (v(t_1))+(v(t_2)) (The ‘average’ stands for average of the quantity over the time interval t_1 to t_2 )

Differentiate the following w.r.t. as indicated: (x^2)/(1+x^2) w.r.t x^2

Find the term(s) indicated in the following case : T_(n)=(T_(n-1))/(T_(n-2)),(ngt2),T_(1)=1,T_(2)=2, T_(6) .

Differentiate the following functions w.r.t.x : sqrt((log(sin(x^2/3 -1)))